146 The UMAP Journal 28. 2 (2007) o Minimizing the waitlist depends on only two variables The modelincorporates HLA values, PRA distributions, no-mismatch prob. bilities, region distribution, and blood-type distribution and compatibility o The model is compatible with alternative strategies, such as a paired ex- stem Model Weaknesses o Remaining lifetime after surgery should be adjusted, since an exponential distribution for remaining lifetime is appropriate only until a certain age o The model cannot account for patients'. We assume that all patients offered kidney take it if the hla value is reasonable, which may not be the case. o The model does not make distinctions for race and socioeconomic status. Different races have differing wait times [Norman 2005, 457] o We assume independence of random variables, so thatincreasing or decreas- ing parameters will not affect other parameters o Ouremphasis on waitlistsizeneglects waitlist time; anotherapproach would be to try to minimize waitlist wait time Tasks 2 and 3: Kidney Paired Exchange Background As noted at the University of Chicago Hospitals, "In 10 to 20 percent of cases at the Hospitals, Patients who need a kidney transplant have family or friends who agree to donate, but the willing donor is found to be biologically unsuited for that specific recipient"[Physicians propose.. 1997] of patient/ donor candidates. Each donor is incompatible with the intended patient but compatible with the other patient. Surgery is performed simulta- neously in the same hospital on four people, with two kidney removals and two kidney transplant However, fornot all patient-donor pairs will the ere be a mutually compatible partner pair. In such a case, it is possible for the cycle to expand to n patient- donor pairs, with each donor giving to a compatible stranger patient(Figure 4) Since such an exchange requires at least 2n surgeons at the same hospital, higher-order exchanges are less desirable on logistic ground A kidney paired exchange program does not affect the intrinsic model out- lined for Task 1. The only change when live incompatible pairs get swapped is146 The UMAP Journal 28.2 (2007) "* Minimizing the waitlist depends on only two variables. "* The model incorporates HLA values, PRA distributions, no-mismatch prob￾abilities, region distribution, and blood-type distribution and compatibility requirements. "* The model is compatible with alternative strategies, such as a paired ex￾change system. Model Weaknesses "* Remaining lifetime after surgery should'be adjusted, since an exponential distribution for remaining lifetime is appropriate only until a certain age. "o The model cannot account for patients'. We assume that all patients offered a kidney take it if the I-LA value is reasonable, which may not be the case. "* The model does not make distinctions for race and socioeconomic status. Different races have differing wait times [Norman 2005, 457]. "o We assume independence of random variables, so that increasing or decreas￾ing parameters will not affect other parameters. "* Our emphasis on waitlist size neglects waitlist time; another approach would be to try to minimize waitlist wait time. Tasks 2 and 3: Kidney Paired Exchange Background As noted at the University of Chicago Hospitals, "In 10 to 20 percent of cases at the Hospitals, patients who need a kidney transplant have family or friends who agree to donate, but the willing donor is found to be biologically unsuited for that specific recipient" [Physicians propose ... 1997]. In the simple kidney paired exchange system (Figure 3), there are two pairs of patient / donor candidates. Each donor is incompatible with the intended patient but compatible with the other patient. Surgery is performed simulta￾neously in the same hospital on four people, with two kidney removals and two kidney transplants. However, for not all patient-donor pairs will there be a mutually compatible partner pair. In such a case, it is possible for the cycle to expand to n patient￾donor pairs, with each donor giving to a compatible stranger patient (Figure 4). Since such an exchange requires at least 2n surgeons at the same hospital, higher-order exchanges are less desirable on logistic grounds. A kidney paired exchange program does not affect the intrinsic model out￾lined for Task 1. The only change when live incompatible pairs get swapped is